Doped graphene emerges as a strong contender for active plasmonic material in mid-infrared wavelengths due to the versatile external control of its permittivity function and also its highly compressed graphene surface plasmon (GSP) wavelength. In this paper, we design active plasmonic waveguide devices based on electrical modulation of doped graphene nanoribbons (GNRs) on a voltage-gated inhomogeneous dielectric layer. We first develop figure-of-merit (FoM) formulae to characterize the performance of passive and active graphene nanoribbon waveguides. Based on the FoMs, we choose optimal GNRs to build a plasmonic shutter, which consists of a GNR placed on top of an inhomogeneous substrate supported by a Si nanopillar. Simulation studies show that for a simple, 50 nm long plasmonic shutter, the modulation contrast can exceed 30 dB. The plasmonic shutter is further extended to build a four-port active power splitter and an eight-port active network, both based on GNR cross-junction waveguides. For the active power splitter, the GSP power transmission at each waveguide arm can be independently controlled by an applied gate voltage with high-modulation contrast and nearly equal power-splitting proportions. From the construct of the eight-port active network, we see that it is possible to scale up the GNR cross-junction waveguides into large and complex active waveguide networks, showing great potential in an exciting new area of mid-infrared graphene plasmonic integrated nanocircuits.
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